We present a continuous formulation of machine learning,as a problem in the calculus of variations and differential-integral equations,in the spirit of classical numerical *** demonstrate that conventional machine lea...
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We present a continuous formulation of machine learning,as a problem in the calculus of variations and differential-integral equations,in the spirit of classical numerical *** demonstrate that conventional machine learning models and algorithms,such as the random feature model,the two-layer neural network model and the residual neural network model,can all be recovered(in a scaled form)as particular discretizations of different continuous *** also present examples of new models,such as the flow-based random feature model,and new algorithms,such as the smoothed particle method and spectral method,that arise naturally from this continuous *** discuss how the issues of generalization error and implicit regularization can be studied under this framework.
computational modeling of neurodynamical systems often deploys neural networks and symbolic dynamics. One particular way for combining these approaches within a framework called vector symbolic architectures leads to ...
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Two-plasmon-decay instability(TPD)poses a critical target preheating risk in direct-drive inertial confinement *** this paper,TPD collectively driven by dual laser beams consisting of a normal-incidence laser beam(Bea...
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Two-plasmon-decay instability(TPD)poses a critical target preheating risk in direct-drive inertial confinement *** this paper,TPD collectively driven by dual laser beams consisting of a normal-incidence laser beam(Beam-N)and a large-angle-incidence laser beam(Beam-L)is investigated via particle-in-cell *** is found that significant TPD growth can develop in this regime at previously unexpected low laser intensities if the intensity of Beam-L exceeds the large-angle-incidence *** beams contribute to the growth of TPD in a“seed-amplification”manner in which the absolute instability driven by Beam-L provides the seeds that are convectively amplified by Beam-N,making TPD energetically important and causing significant pump depletion and hot-electron generation.
The multiconfiguration Dirac-Hartree-Fock method implemented in the Grasp2018 package was employed to calculate the magnetic dipole hyperfine interaction constants and electric field gradients of levels in the ground ...
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Basic recursive summation and common dot product algorithm have a backward error bound that grows linearly with the vector dimension. Blanchard [1] proposed a class of fast and accurate summation and dot product algor...
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In this paper we analyze the graph-based approach to semi-supervised learning under a manifold assumption. We adopt a Bayesian perspective and demonstrate that, for a suitable choice of prior constructed with sufficie...
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In this paper we analyze the graph-based approach to semi-supervised learning under a manifold assumption. We adopt a Bayesian perspective and demonstrate that, for a suitable choice of prior constructed with sufficiently many unlabeled data, the posterior contracts around the truth at a rate that is minimax optimal up to a logarithmic factor. Our theory covers both regression and classification.
Convection-dominated singularly perturbed problems are a special type of differential equations that arise in various natural phenomena such as fluid dynamics. Hence, these problems need special consideration in the l...
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A Bayesian network approach is presented for probabilistic safety analysis(PSA)of railway *** idea consists of identifying and reproducing all the elements that the train encounters when circulating along a railway li...
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A Bayesian network approach is presented for probabilistic safety analysis(PSA)of railway *** idea consists of identifying and reproducing all the elements that the train encounters when circulating along a railway line,such as light and speed limit signals,tunnel or viaduct entries or exits,cuttings and embankments,acoustic sounds received in the cabin,curves,*** addition,since the human error is very relevant for safety evaluation,the automatic train protection(ATP)systems and the driver behaviour and its time evolution are modelled and taken into account to determine the probabilities of human *** nodes of the Bayesian network,their links and the associated probability tables are automatically constructed based on the line data that need to be carefully *** conditional probability tables are reproduced by closed formulas,which facilitate the modelling and the sensitivity analysis.A sorted list of the most dangerous elements in the line is obtained,which permits making decisions about the line safety and programming maintenance operations in order to optimize them and reduce the maintenance costs *** proposed methodology is illustrated by its application to several cases that include real lines such as the Palencia-Santander and the Dublin-Belfast lines.
We explore the relationship between complexity and duality in quantum systems, focusing on how local and non-local operators evolve under time evolution. We find that non-local operators, which are dual to local opera...
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This paper investigates a novel nonlinear singular fractional SI model with the Φp operator and the Mittag-Leffler kernel. The initial investigation includes the existence, uniqueness, boundedness, and non-negativity...
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